Thermo Sudoku — short for Thermometer Sudoku — is a classic 9x9 Sudoku decorated with thermometer shapes. Along every thermometer, the digits must strictly increase from the round bulb to the tip. The standard row, column, and box rules still apply, so Thermo combines familiar Sudoku logic with a clean, visual ordering constraint. Because each cell's spot on a thermometer limits which digits can go there, the shapes are as much a help as a hurdle: long thermometers practically solve themselves.
What is Thermo Sudoku?
Thermo Sudoku is played on the same 9x9 grid as standard Sudoku, with a handful of thermometer shapes overlaid on the cells. A thermometer is an ordered path of orthogonally adjacent cells (horizontal or vertical steps). One end is drawn as a large filled circle — the bulb — and the line narrows toward the tip at the other end. The single rule attached to every thermometer is that the digits get bigger as you travel from the bulb to the tip, with no ties allowed. Each puzzle has one unique solution reachable by pure logic.
Thermo Sudoku Rules
- Standard Sudoku rules: Each row, each column, and each 3x3 box must contain the digits 1 through 9 exactly once.
- Thermometer rule: Digits along a thermometer must strictly increase from the bulb to the tip.
- No ties: Equal digits are never allowed anywhere on the same thermometer — each step must be at least one larger.
- The bulb is smallest: The large circle always holds the smallest digit on its thermometer, and the tip always holds the largest.
Position Bounds: The Heart of Thermo Logic
Because a thermometer strictly increases, a cell's position on it already restricts its digit before you consider any other clue. On a thermometer of length L, number the cells from the bulb starting at 0. The cell at index i must be:
- at least i + 1 — there are i strictly smaller digits crammed in before it, and
- at most N − (L − 1 − i) — it must leave room for the strictly larger digits after it, where N is the grid size (9 here).
| Position on a 5-cell thermometer (9x9) | Possible digits |
|---|---|
| Bulb (index 0) | 1–5 |
| Index 1 | 2–6 |
| Index 2 | 3–7 |
| Index 3 | 4–8 |
| Tip (index 4) | 5–9 |
Solving Strategies
1. Start with the longest thermometers
Length is constraint. A five-cell thermometer only allows the digit runs shown above, and the more filled cells or crossing rows and columns it has, the faster it collapses to a single option. Scan for the longest thermometers first and pencil in each cell's position window.
2. Squeeze from both ends
Work the bulb and the tip together. If the bulb can't be 1 (say a 1 already sits in its box), every cell above it shifts up by one, and the whole thermometer's windows narrow. Likewise, capping the tip pushes the earlier cells down. Alternating between the two ends is the classic thermometer "squeeze."
3. Use crossing constraints
A thermometer that passes through the same row, column, or box twice can never repeat a digit there anyway — and since it already can't repeat along its length, those crossings combine to eliminate candidates quickly. Watch where a thermometer re-enters a box.
4. Combine with standard Sudoku logic
Position bounds narrow candidates; classic techniques place them. Alternate thermometer deductions with naked singles, hidden singles, pointing pairs, and box-line reduction from our solving techniques library. Each unlocks the other.
Mini Thermo (6x6)
Mini Thermo brings the same increasing-thermometer rule to a compact 6x6 grid using the digits 1 through 6 with 2x3 boxes. The rules are identical, and the small range makes position bounds crystal clear: a five-cell thermometer can only be 1-2-3-4-5 or 2-3-4-5-6, and a six-cell thermometer is fully forced to 1-2-3-4-5-6. Mini Thermo is the ideal place to internalise thermometer logic — read the full Mini Thermo Sudoku guide or jump straight into the playable 6x6 board.
Tips for Beginners
- Always pencil the position window. Before anything else, mark each thermometer cell's min–max range. Half your deductions fall out of that step alone.
- The bulb is never the biggest. A bulb can never hold 9 (or 6 on a mini), and a tip can never hold 1.
- Long beats short. Spend your attention on the longest thermometers; short three-cell ones give the least information.
- Watch for the fully-forced thermometer. A length-9 thermometer on a 9x9 grid is 1–9 in order, no thinking required.
- Start on the 6x6 mini. The same logic is far easier to see on six digits. Build confidence there first.
- Never guess. Every Thermo puzzle has a unique logical solution. If you stall, re-check a long thermometer's windows.
Thermo Sudoku rewards a feel for ordering rather than arithmetic. Once you learn to read each cell's position window and squeeze the long thermometers from both ends, the shapes turn from decoration into a precise solving path. Start small with Mini Thermo, and the full 9x9 puzzles will soon feel approachable.